I have some italian software and it has a sentence that says "Il panino e nel piatto" but I read that as "the sandwich is in the plate". Shouldn't it be "Il panino e sul piatto" or, "the sandwich is on the plate"?

“Il panino è nel piatto” (you must put a grave accent on “è”; it’s a verb not a conjunction) is correct. It’s food and that’s its natural place. The preposition “on” (su, sopra) would be used if the sandwich was put on, say, a table, a napkin, etc. But let’s suppose the plate was upturned; in this case we could say, “Il panino è sul piatto.”
If it was in a lunch basket/box, in a school bag, in a rucksack, etc. you could say “in” (in, inside):